Mr Venner, 78, walked up to the altar of Notre-Dame, one of the most-visited attractions in France, and shot himself in the mouth with a single-shot pistol on Tuesday afternoon, in front of some 1,500 visitors.

About 100 sympathisers later gathered outside the cathedral to pay tribute to the former Algerian War veteran and far-right militant, who had made a career writing history books.

'Protest against decay'

"All respect to Dominique Venner whose final, eminently political act was to try to wake up the people of France," Ms Le Pen wrote on Twitter.

"It is in life and hope that France will renew and save itself," she later added.

Bruno Gollnisch, another National Front member, said Mr Venner's "dramatic act was a protest against the decay of our society".

The police said Mr Venner had made no statement before killing himself, although a note was found next to his body. They did not disclose its contents.

Just hours earlier, Mr Venner had bitterly criticised the same-sex marriage act on his blog, saying it was as "disastrous" for France as the prospect of Islamist rule.

After his death, a friend read out a message from the dead man on a conservative radio station, Radio Courtoisie, where he used to broadcast.

"I believe it is necessary to sacrifice myself to break with the lethargy that is overwhelming us," he was quoted as saying in the message.

"I am killing myself to awaken slumbering consciences."

Mr Venner once served time in prison for his activities with the Secret Army Organisation (OAS), which opposed Algerian independence in the early 1960s and tried to assassinate President Charles De Gaulle.

The BBC's Christian Fraser in Paris says Notre-Dame attracts more than 13 million visitors each year, but security is relatively relaxed. It would not be difficult to conceal a weapon in a shoulder bag, he says.

The rector of Notre-Dame, Monsignor Patrick Jacquin, said it appeared to be the first suicide in decades at the cathedral. A few people had jumped to their deaths from Notre-Dame's twin towers, but no-one was thought to have killed themselves at the altar before, he added.

Mr Venner's death sharply divided opinion on social media in France. On Twitter, most of the comments appeared to be negative, with some dismissing his suicide as an act of "terrorism" or labelling him a "Nazi". Others expressed admiration, with one describing him as a patriot who had died "for his fatherland and its lost values".